In the work entitled “Theory of Law and State in Connection with the Theory of Morality” L. Petrażycki inspired by his emotive theory of law formulated a number of theoretical and legal considerations relating to understanding of the essence of a norm in law and moral. According to these considerations, a norm is a two-agent imperative and attributive relation and its structure differs depending on whether it is a norm of law or a moral norm. Based on such understanding of a norm, L. Petrażycki outlined a general classification of norms of law and moral as special normative relations. Several years after publishing these ideas of L. Petrażycki, a famous American legal scientist W. Hohfeld proposed a concept of systematization of legal notions which reflect two-agent normative relations. Hohfeld's concept is based on the idea that every legal relation is bilateral, it involves two relations and connects two parties in a certain way. E.g., if one of the parties has a right to something - a power or a benefit - then there is another party to this legal relation for which it is an obligation ensuring the right of the first party, a liability strengthening its power or absence of the right to restrict its benefit. W. Hohfeld was not aware of Petrażycki's ideas. Hohfeld's ideas have become classical in the foreign legal theory and influenced the development of deontic logic as well. It can not be said about Petrażycki's ideas which were primarily known to researchers in the sphere of the theory and philosophy of law. This article attempts to demonstrate two provisions regarding Petrażycki's and Hohfeld's doctrines. The first one is of a historical and scientific character, while the second one refers to the logical aspects of law. The first provision is that Petrażycki's interpretation of a norm as a set of special normative relations between different parties, as well as the relevant classification of norms as relations in law and moral constitute, essentially, a conceptual foundation of the classification of legal notions of normative relations proposed by W. Hohfeld. In other words, Petrażycki's ideas about the structure of a norm, its functional peculiarities in relation to law constitute a sort of a general classification of normative relations of W. Hohfeld. Thus, the author shows that Petrażycki, rather than Hohfeld, was first to create a concept of a norm as a relation in law and morality. In this regards, the author distinguishes between a normative relation as an establishment of a certain social connection between parties and a legal relation. According to this distinction, every legal relation is also a normative relation. However, normative relations are not reduced to legal relations, but include other types of relation, such as moral ones. Moreover, the author distinguishes the norm establishing a certain normative relation and a logical structure of the norm which can specify formal connections within the norm. The second provision is that, from the logical point of view, expressiveness of standard deontic logic is insufficient to create formalisms on the basis of classification of norms by L. Petrażycki or on the basis of classification of legal concepts of normative relations by W. Hohfeld.